SSC CGL Previous Paper (Held On: 9 March 2020 Shift 2) (Previous Year Paper)

The correct mirror image of the given letter-Cluster when a vertical mirror is placed on the right side of the cluster is,

Hence, option 2 is the correct answer.

The pattern followed is,

Column wise:

(Number 1)² – (Number 2)² = Number 3

For Column 1:

15² – 8²

225 – 64 = 161

For Column 2:

18² – 9²

324 – 81 = 243

For Column 3:

24² – 12²

576 – 144 = 432

Hence, “24” is the correct answer.

The pattern followed is,

Hence, “R” is the correct answer.

Casting comes first in the order.

Casting is followed by Acting.

Acting is followed by Film shooting.

Film shooting is followed by Editing.

Editing is followed by Final film.

The correct logical order is,

Casting (1) → Acting (2) → Film shooting (3) → Editing (5) → Final film (4)

Hence, option 2 is the correct answer.

Temple is a holy place of worship.

Similarly,

Option 1 → President is the highest position in the university.

Option 2 → Garden is a place where plants are found.

Option 3 → Church is a holy place for prayer.

Option 4 → Golden Temple is a holy place of worship in Amritsar.

‘Church: prayer’ share the same relationship as that shared by the given pair of words.

Hence, “church: prayer” is the correct answer.

According to the given figure,

‘1’ lies opposite to ‘4’

‘3’ lies opposite to ‘5’

And,

‘2’ lies opposite to ‘6’

From the given dice,

Only A and B follow the above conditions.

Hence, “only A and B” is the correct answer.

The pattern followed is,

(22, 64, 352)

22 × 16 = 352

64 × 5 + (64/2) = 352

Similarly,

Option 1 → (24, 16, 108) → 108 is not divisible by 24

Option 2 → (14, 68, 238) → 14 × 17 = 238

68 × 3 + (68/2) = 238

Option 3 → (27, 52, 453) → 453 is not divisible by 27

Option 4 → (19, 52, 257) → 257 is not divisible by 19

‘(14, 68, 238)’ is related in the same way as are the numbers in the given set.

Hence, “(14, 68, 238)” is the correct answer.

Alternate MethodLOGIC: (First Number × Second Number) ÷ 4 = Third Number

In (22, 64, 352) →

(22 × 64) ÷ 4 = 1408 ÷ 4 = 352

Similarly;

In (14, 68, 238) →

(14 × 68) ÷ 4 = 952 ÷ 4 = 238

Hence, "238" is the correct answer.

Mothers can also be Lady Constables.

And,

Uncles are represented separately.

The correct Venn diagram is,

Hence, option 1 is the correct answer.

The number of triangles in the given figure is,

Hence, “13” is the correct answer.

The given figure is embedded in,

Hence, option 2 is the correct answer.

The pattern followed is,

For SPECIAL,

The place value of S is 19, 19 + 1 = 20

The place value of P is 16, 16 + 1 = 17

The place value of E is 5, 5 + 1 = 6

The place value of C is 3, 3 + 1 = 4

The place value of I is 9, 9 + 1 = 10

The place value of A is 1, 1 + 1 = 2

The place value of L is 12, 12 + 1 = 13

So

SPECIAL is coded as ‘20176410213’

Similarly,

For MACHINE,

The place value of M is 13, 13 + 1 = 14

The place value of A is 1, 1 + 1 = 2

The place value of C is 3, 3 + 1 = 4

The place value of H is 8, 8 + 1 = 9

The place value of I is 9, 9 + 1 = 10

The place value of N is 14, 14 + 1 = 15

The place value of E is 5, 5 + 1 = 6

MACHINE is coded as ‘1424910156’

Hence, “1424910156” is the correct answer.

The pattern followed is,

All follow the same pattern, except ‘KN’.

Hence, “KN” is the odd letter cluster.

Photoshop is an image – editing software used to edit images digitally.

Similarly,

An optical is an advanced hardware computer pointing device that uses light emitting diodes.

Hence, “hardware” is the correct answer.

The pattern followed is,

Option 1 → 21 : 154 → 21 : 21 × 7 + 7

Option 2 → 39 : 270 → 39 : 39 × 7 – 3

Option 3 → 31 : 214 → 31 : 31 × 7 – 3

Option 4 → 37 : 256 → 37 : 37 × 7 – 3

All follow the same pattern, except ’21 : 154’.

Hence, “21 : 154” is the number – pair that is different.

The pattern followed is,

Similarly,

Hence, “CYLGNIRE” is the correct answer.

The pattern followed is,

3 : 3³ + 3³ – 3

3 : 27 + 27 – 3

3 : 54 – 3

3 : 51

Similarly,

7 : 7³ + 7³ – 7

7 : 343 + 343 – 7

7 : 686 – 7

7 : 679

‘679’ is related to the third number in the same way as the second number is related to the first number.

Hence, “679” is the correct answer.

Interchanging the signs and using BODMAS rule,

Option 1 → × and ÷

14 ÷ 3 × 27 + 54 – 9 = 21

4.6 × 27 + 54 – 9 = 21

124.2 + 54 – 9 = 21

178.2 – 9 is not equal to 21

Option 2 → + and –

14 × 3 ÷ 27 – 54 + 9 = 21

14 × 1/9 – 54 + 9 = 21

1.5 – 54 + 9 = 21

10.5 – 54 is not equal to 21

Option 3 → × and –

14 - 3 ÷ 27 + 54 × 9 = 21

14 – 1/9 + 54 × 9 = 21

14 – 0.11 + 486 = 21

500 – 0.11 is not equal to 21

Option 4 → ÷ and –

14 × 3 - 27 + 54 ÷ 9 = 21

14 × 3 – 27 + 6 = 21

42 – 27 + 6 = 21

48 – 27 = 21

21 = 21

Hence, option 4 is the correct answer.

Note: Multiple of 400 years i.e. 800, 1200, 1600, 2000 have 0 odd days.

Calculating leap year: For Finding number of leap year (1-99)yr, divide the number of years by 4 and the quotient will be the number of leap year.

Code for week days

Total odd days = 0 + 4 + 0 + 5 = 9 days = 1 week + 2 odd days

2 is the code for "Tuesday"

29 June, 2010 is Tuesday.

Hence, “Tuesday” is the correct answer.

The pattern followed is,

Hence, “NAVIICTE” is the correct answer.

The pattern followed is,

Hence, “99” is the correct answer.

Drawing the Venn diagram,

Conclusion 1: No park is a garden → True (This is definitely true)

Conclusion 2: Some schools are gardens → True (This is definitely true)

Conclusion 3: Some parks are gardens → False (This is definitely false)

Hence, “only conclusions 1 and 2” follow.

Drawing the diagram for ‘Y × M – T – Z ÷ L × U’,

U is the mother – in – law to Y.

Hence, “mother – in – law” is the correct answer.

Diabetes, Cancer and Asthma are diseases.

Whereas,

Bone marrow is the spongy tissue inside some of the bones in the body, including the hip and thigh bones.

Hence, “bone marrow” is the odd word.

The paper when unfolded look like,

Hence, option 3 is the correct answer.

The pattern followed is,

The symbols in the given figure are moving in the following manner:

North-west → Centre → North-east → South-east → South-west.

The symbol in the northwest corner is placed at the centre in the image which comes next and a new symbol is added to the northwest corner in each figure.

The image which will come next in the pattern is,

Hence, option 2 is the correct answer.

Siraj-ud-Daula signed the treaty of Alinagar with the British.

• On 9 February 1757, the Treaty of Alinagar was concluded between Robert Clive of the British East India Company and  Muhammad Siraj Ud Daul Mirza(the Nawab of Bengal).
• On the basis of the terms of the deal, the Nawab would accept all the provisions of the 1717 Farmman of Mughal Emperor Farrukh Siyar. In fact, all British goods going through Bengal should be excluded from customs duty.
• Siraj ud-Daulah was Bengal's last independent Nawab. The end of his reign marked the beginning of the British East India Company's control over Bengal and, later, almost all of India.
• Robert Clive was the first British governor to occupy the Bengal presidency.
• He started as an officer of the British Army and the East India Company (EIC) who established the military and political hegemony of the EIC by taking possession of Bengal.

The Ravi River was known as Purushni in the Vedic period.

• The River Ravi is a transboundary river that connects northwest India and East Pakistan.
• This is one of the six rivers of the Punjab Indus basin (Punjab means "five rivers").
• The Ravi waters are assigned to India under the Indus Waters Treaties.
• It originates in the Himalayas of the Multan Tehsil district of Kangra, Himachal Pradesh, India.

India has been ranked 129th in the Human Development Index 2019.

• The top three positions in the index were taken by Norway, Switzerland and Ireland.
• According to the report, South Asia was the fastest-growing region in human development, with 46% growth in 1990-2018, followed by 43% in East Asia and the Pacific.
• The Indian HDI value rose from 0.431 to 0.647.
• The Human Development Index tests average country achievement in three fundamental aspects of human growth, i.e. life expectancy, education and per capita income.
• It is officially released by the United Nations Development Programme (UNDP).

Constantan is an alloy of copper and nickel.

• It normally consists of 55% copper and 45% nickel.
• Its key characteristic is the low thermal variation of its resistance, which is consistent over a large range of temperatures.
• It was discovered by Edward Weston in 1887.
• It is often used to form thermocouples with wires made of iron, copper, or chromium.
• It has an extremely strong negative Seebeck coefficient above 0 degree Celsius, resulting in good temperature sensitivity.

The Mughal Emperor Akbar initiated "Din-i-Elahi".

• This was meant to combine some of the components of the faiths of his empire, and thereby to resolve the contradictions that separated his subjects.
• The components were derived mainly from Islam and Hinduism, although some others were also taken from Buddhism, Jainism and Zoroastrianism.
• Birbal was the first follower of the Din -i-Elahi.
• Akbar the Great was the third Mughal emperor to rule from 1556 to 1605. Akbar succeeded his father, Humayun, under the emperor, Bairam Khan.

In ITCZ, "C" is stand for Convergence.

• The Intertropical Convergence Zone (ITCZ) is the zone that covers the Earth, near the equator.
• Where trade winds from the Northern and Southern Hemispheres come together.
• The sun and warm water of the equator heat up the air in the ITCZ, increase its temperature, and keep it buoyant.
• With the aid of the convergence of the industrial winds, the buoyant air is rising.
• When the air increases, it spreads and cools, releasing concentrated heat in an almost endless cycle of thunderstorms.

PU Zoramthanga is the Chief Minister of Mizoram as on November 2019.

• He is the leader of the Mizo National Front (MNF).
• From December 1998 to December 2008 he served as Chief Minister of Mizoram for two consecutive terms.
• He was re-elected as a Member of the Legislative Assembly in 2018 by the Aizawl East-I Constituency and became 5th Chief Minister of Mizoram on 15 December 2018.
• Laldenga was the first Chief Minister of Mizoram from 1986 to 1988.
• Conrad Kongkal Sangma is the current Chief Minister of Meghalaya.
• Neiphiu Rio is the current Chief Minister of Nagaland.

The Correct Answer is Option 3 i.e Arise

• In 2019, IIT-Madras launched the country's first indigenously designed standing wheelchair 'Arise'.
• The standing wheelchair was launched in the presence of Union Minister of Social Justice and Empowerment Thawarchand Gehlot.
• It enables a differently-abled person requiring a wheelchair to shift from sitting to standing position, and vice versa, independently and in a controlled manner

The rating for a fuse used in a household electric circuit is provided on the basis of the current.

• The fuse is used to provide overcurrent protection.
• The main component is a metal wire or strip that melts when too much current flows through it, stopping or interrupting the current.
• It is a sacrificial device; once the fuse has been operated, the open circuit must be replaced or rewired, depending on the type.
• The Wiring Regulations usually define the maximum current rate of fuse for particular circuits.
• Short circuits, overload, uneven loads, or device failure are the primary or some of the reasons for fuse operation.

India won six medals in the 2012 Summer Olympics.

• It was held in London from 27th July to 12th August 2012.
• In total, 83 athletes, 60 men and 23 women, competed in 13 sports.
• Badminton player and world junior champion Saina Nehwal became the first Indian athlete to win the bronze medal in women's singles.
• Wrestler and Olympic bronze medalist Sushil Kumar were able to win another medal by winning silver in men's freestyle wrestling.
• He was also appointed by the Indian Olympic Association as the flag bearer of the nation at the opening ceremony.
• Mary Kom was the flag bearer of the nation at the closing ceremony.

Ministry of Rural Development is NOT associated with the initiative of Beti Bachao, Beti Padhao Scheme.

• Beti Bachao, Beti Padhao is a Government of India initiative aimed at raising awareness and increasing the quality of child welfare programs in India.
• It was launched by PM Narendra Modi on 22 January 2015.
• On 26 August 2016, the 2016 Olympics Bronze Medalist Sakshi Malik was named BBBP Brand Ambassador.
• This is primarily targeted at regions in Uttar Pradesh, Haryana, Uttarakhand, Punjab, Bihar and Delhi.
• Ministry of Health and Family Welfare, Ministry of Women and Child Development and Ministry of Human Resource Development has initiated this scheme.

Turtle Olly was the mascot of the Men's Hockey World Cup held at Bhubaneswar in 2018.

• The official mascot of the event was introduced by the Sports and Youth Services Department.
• The World cup was started from November 28 to December 16.
• It was 14th edition of World cup which won by the Belgium first time and Netherlands was the runner-up of this tournament.
• Shera was the mascot of the Commonwealth Games, 2010.
• Borobi was the mascot of the Commonwealth Game, 2018.
• Millie was the mascot of the Summer Olympics, 2000.

Partition of Bengal did not take in 1919.

• The first partition of Bengal was the administrative reorganization of the Bengal Presidency carried out by the British Raj authorities in 1905.
• On 16 October 1905, after being proclaimed on 19 July 1905 by the Viceroy of India of that time, Lord Curzon, the partition divided the largely Muslim eastern regions from the largely Hindu western regions.
• Bengal, Bihar, parts of Chhattisgarh, Orissa, and Assam were part of the Bengal Presidency.

'Pedology' is the study of soil.

• It's one of the two primary fields of soil science, the other being edaphology.
• Pedology deals with pedogenesis, soil ecology, and soil selection, while edaphology explores how soils affect plants, fungi, and other living things.
• The quantitative field of pedology is referred to as pedometrics.
• Dermatology is a field of medicine that deals with the skin.
• Pediatric is a field of medicine that deals with childhood illness.
• Hydrogeology is the study of groundwater.

Plastic is a non-biodegradable waste.

Key Points

• Non-biodegradable material can be characterized as a category of substance that can not be broken down by natural organisms and acts as a source of pollution.
• Non-biodegradable waste is a waste that can not be decomposed or dissolved by natural chemicals.
• They have existed on earth for thousands of years without any deterioration.
• Dead animals, Vegetables and Flowers are the biodegradable waste.
• Biodegradable material can be described as a substance that can be decomposed by bacteria or other natural organisms and does not contribute to pollution.
• Biodegradable waste is waste material that is and can be contaminated by natural causes such as organisms (e.g. bacteria, fungi, etc.), abiotic elements such as temperature, UV, oxygen, etc.

The 101^st Amendment of the Constitution of India imposed the Goods and Services Tax(GST).

• This amendment introduced the National Goods and Services Tax (GST) in India as of 1st July 2017.
• It was adopted as the One Hundred and Twenty-Second Amendment Bill to the Constitution of India.
• The Goods and Services Tax (GST) is a value-added tax (VAT) imposed as a systematic indirect tax levy on the production, sale, and use of products and services at the national level.
• It shall absorb all indirect taxes imposed on goods and services by the central and state governments of India.

Assam does NOT share its boundary with Nepal.

• The boundary between India and Nepal is an open international border between India and Nepal.
• The 1,690 km (1,050.12 mi) long boundary covers the Himalayan and Indo-Gangetic areas.
• The current form was formed in the aftermath of the Sugaul Treaty of 1816 between Nepal and the British Raj.
• Uttarakhand, Uttar Pradesh, Sikkim, West Bengal and Bihar shares their border with Nepal.

"Revolution 2020" is written by Chetan Bhagat in 2011.

• The story is about the triangle of passion, greed, and the journey of self-discovery.
• The author claimed that the novel was based on the "rampant corruption" visible in the Indian youth education system, with the choice of Varanasi as a setting arising from "a special link to the city" following his visit.
• Chetan Bhagat is an Indian author of English novels.
• He was included in Time Magazine's list of the 100 Most Influential People of the world in 2010.
• The debut novel of Chetan bhagat is the Five Points someone(2014).

In July 2019, Jal Shakti Abhiyan scheme was launched to accelerate water harvesting and conservation measures.

• It was a time-bound, mission-mode water conservation campaign.
• The JSA was conducted in two phases: phase 1 from 1 July to 15 September 2019 for all States and Union Territories; and phase 2 from 1 October to 30 November 2019 for States and UTs receiving the withdrawing monsoon (Andhra Pradesh, Karnataka, Puducherry and Tamil Nadu).
• During the initiative, ministers, irrigation experts and scientists from the Government of India collaborated with state and district authorities in India's most water-stressed districts * on water conservation and water quality management by concentrating on rapid execution of five target initiatives.
• The goal of the JSA is to render water conservation Jan Andolan through the construction of assets and comprehensive communication.

The festival of Uttarayan is celebrated in Gujarat.

Key Points

• This festival is also known as Makar Sankranti.
• It is a festival day in the Hindu calendar, devoted to the God of Surya (Sun).
• It is celebrated every year in the lunar month of Magha, which corresponds to the month of January according to the Gregorian calendar, and is the day when the people of India celebrate their harvest.
• It is the first day of the transit of the sun to Makara (Capricorn), marking the end of the month with the winter solstice and the beginning of longer days.
• In other states this festival is also known as Magh Bihu in Assam, Maghi (preceded by Lohri) in Punjab, Haryana and Himachal Pradesh.

The Correct Answer is Option 3 i.e Jataka Tales.

Key Points

• The paintings of Ajanta caves predominantly narrate the Jataka tales.
• The Jatakas are an important part of Buddhist art and literature.
• They are examples of rock-cut temples.
• It consists of thirty caves, each dedicated to the life of the Buddha.
• The Ajanta Caves have been a UNESCO World Heritage Site in 1983.
• The caves are believed to be made in 2 distinct periods:

1. Satavahana period
2. Vakataka period

Additional Information

• ​The Ajanta Caves are a series of 29 Buddhist cave temples in Ajanta, India, some of which date from the 2nd century BC. Encompassing both Theravada and Mahayana Buddhist traditions, the Ajanta caves preserve some of the best masterpieces of Buddhist art in India.
• The Ajanta Caves were carved in the 2nd century BC out of a horseshoe-shaped cliff along the Waghora River.

India has the rank of 141 in the Global Peace Index 2019.

• India got this position among 163 countries.
• Iceland has the most peaceful country while Afghanistan has the least peaceful nation.
• India, the United States, China, Saudi Arabia and Russia are the top five countries with the highest overall military spending.
• The Global Peace Index (GPI) tests current internal and international violence, stability and protection in society, and the degree of militarisation in 163 countries and territories, taking into account 23 indices.
• It is a study created by the Institute for Economics and Peace (IEP) and assembled in collaboration with an international panel of peace experts from peace organisations and think tanks with data gathered and compiled by the Economist Intelligence Unit.

• 2 molecules of ATP are obtained by the anaerobic respiration of one molecule of glucose.
• Respiration is a glucose degradation mechanism with the aid of molecular oxygen to generate ATP.
• It requires both glycolysis and phosphorylation.
• Glycolysis is the first step of glucose degradation that occurs in the absence of oxygen and transforms one glucose molecule into two pyruvate molecules.
• During this cycle, 4 ATP molecules are generated and 2 ATP molecules are consumed.

Medha Patkar is NOT a recipient of the 2019 Mother Teresa Memorial Awards for Social Justice.

• In 2014, She was awarded Mother Teresa Memorial Awards for Social Justice.
• She is an Indian social activist focusing on a variety of main political and economic problems faced by minorities, Dalits, fishermen, workers, and women suffering oppression in India.
• The Mother Teresa Memorial Awards are given in honor of Mother Teresa.
• The aim to encourage the socialist for justice and peace. This award was given since 2005.
• Kailash Satyarthi, Priti Patkar, and Ajeet Singh were recipients of this award in 2019.

The troposphere is the lowermost layer of the Atmosphere.

• It comprises 75% of the mass of the atmosphere and 25% of the total mass of water vapour and aerosols.
• The maximum height of the troposphere is 18 km in the tropics, 17 km in the middle latitudes and 6 km in the polar regions during the winter.
• The maximum average height of the troposphere is 13 km.

Total expenditure on all the items in 2014 = 284 + 98 + 3 + 23.4 + 74 = 482.4

Total expenditure on all the items in 2018 = 425 + 141 + 3.96 + 49.4 + 108 = 727.36

Required percentage = 482.4/727.36 × 100 = 66.32%

a = 2b = 8c

Let a = 2b = 8c = k

a = k

2b = k

⇒ b = k/2

8c = k

⇒ c = k/8

Ratio of a : b : c = k : k/2 : k/8 = 8 : 8k/2 : 8k/8 = 8 : 4 : 1

Now,

$\frac{{\sqrt {{a^2} + {b^2} + {c^2}} }}{{2c}}$

$\Rightarrow \frac{{\sqrt {{8^2} + {4^2} + {1^2}} }}{2}$

$\Rightarrow \frac{{\sqrt {64 + 16 + 1} }}{2}$

⇒ √81/2

⇒ 9/2

Short Trick:

a = 2b = 8c

a : b : c = 1 : 1/2 : 1/8 = 8 : 4 : 1

Now,

$\frac{{\sqrt {{a^2} + {b^2} + {c^2}} }}{{2c}}$

$\Rightarrow \frac{{\sqrt {{8^2} + {4^2} + {1^2}} }}{2}$

$\Rightarrow \frac{{\sqrt {64 + 16 + 1} }}{2}$

⇒ √81/2

⇒ 9/2

As we know,

Angle is directly proportional to opposite side length

Hence, ∠C < ∠B < ∠A

Given:-

 $\frac{{2sin{{22}^0}}}{{cos{{68}^0}}} - \frac{{2cot{{75}^0}}}{{5tan{{15}^0}}} - \frac{{8tan{{45}^0}tan{{20}^0}tan{{40}^0}tan{{50}^0}tan{{70}^0}}}{5}$ 

Concept used:

Calculation:

$\frac{{2sin{{22}^0}}}{{cos{{68}^0}}} - \frac{{2cot{{75}^0}}}{{5tan{{15}^0}}} - \frac{{8tan{{45}^0}tan{{20}^0}tan{{40}^0}tan{{50}^0}tan{{70}^0}}}{5}$

$\Rightarrow \frac{{2sin{{22}^0}}}{{sin{{22}^0}}} - \frac{{2cot{{75}^0}}}{{5cot{{75}^0}}} - \frac{{8;tan{{45}^0}tan{{20}^0}tan{{40}^0};cot{{20}^0}cot{{40}^0}}}{5}$

⇒ 2 – 2/5 – 8/5

⇒ (10 – 2 – 8)/5

⇒ 0/5

⇒ 0

Using allegation method

20% - 10%

0%

10 : 20

Ratio of first book to second book = 10 : 20 = 1 : 2

1 + 2 = 3 unit

⇒ 3 unit = 300

⇒ 1 unit = 100

CP of the first book = Rs. 100

∴ SP of the first book = 100 × 120/100 = Rs. 120

Alternate Method 

Let CP of both books 100x and 100y respectively.

One is sells at 20% and other at 10% loss. There is no loss no profit means profit from one book is equal to loss from second book.

Profit from one book = 20% of 100x = 20x

Loss from other book = 10% of 100y = 10y

So

20x = 10y

⇒ x/y = 1/2

And we know total cost of both books is Rs. 300,

100x + 100y = 300

⇒ x + y = 3

So 

x = 1

y = 2

cost price of book which sells at profit = 100 * 1 = Rs. 100

SP of book which sells at profit = 120% of 100 = Rs. 120

Given:

5cotθ = 3

$\frac{{6sin{\rm{θ }} - 3{\rm{cosθ }}}}{{7sin{\rm{θ }} + 3{\rm{cosθ }}}}$ =?

Calculation:

5cotθ = 3

⇒ cotθ = $5\over3$

$\frac{{6sin{\rm{θ }} - 3{\rm{cosθ }}}}{{7sin{\rm{θ }} + 3{\rm{cosθ }}}}$

⇒ ${sin\theta{(6 - 3{cos\theta\over sin\theta})}}\over{sin\theta{(7+3{cos\theta\over sin\theta})}}$ 

⇒ $\frac{{6 - 3{\rm{cotθ }}}}{{7 + 3{\rm{cotθ }}}}$ = $\frac{{6 - 3 × \frac{3}{5}}}{{7 + 3 × \frac{3}{5}}}$

⇒ $\frac{{6 - \frac{9}{5}}}{{7 + \frac{9}{5}}}$ = $\frac{{\frac{{21}}{5}}}{{\frac{{44}}{5}}}$

⇒ $21\over5$ × $5\over44$ = $21\over44$

Let n = 7, then condition satisfied.

Hence, 7n = 7 × 7 = 49

Now, 49 ÷ 5, then remainder is 4.

Let the number be 5x.

Then, The integer n = 5x + 2

Take x = 1 

Then, n = 7

The value of 7n = 49

49 divided by 5 leaves the remainder 4

∴ 4 is the remainder if 7n is divided by 5.

Given:

x + y = 13, y + z = 15 and z + x = 16

Calculation:

Adding all given equations, we get

2(x + y + z) = 44

⇒ x + y + z = 22

Hence, x = 22 – 15 = 7

y = 22 – 16 = 6

and, z = 22 – 13 = 9

Now,

(xy + xz)/xyz

⇒ (y + z)/yz

⇒ 15/(6 × 9)

⇒ 5/18

11 + 11 × 11 – 11 ÷ 11

⇒ 11 + 121 – 1

⇒ 131

Let MP of the bat be Rs. x

According to the question

92x/100 – 90x/100 = 70

⇒ 2x = 7000

⇒ x = 3500

Short Trick:

Let MP of the bat be 100%

10% - 8% = 70

⇒ 2% = 70

⇒100% = 3500

As we know,

Ratio of volume of sphere of A to B = (4/3) π(R₁)³ : (4/3) π(R₂)³ = (R₁)³ : (R₂)³

According to the question

(R₁/R₂)³ = 125/64

R₁/R₂ = ∛125/64 = 5/4

R₁ : R₂ = 5 : 4

Now, 5 + 4 = 9 units

⇒ 9 units = 36

⇒ 1 unit = 4

Hence, 5 units = 5 × 4 = 20 cm

Radius of sphere A = 20 cm

Total surface area of sphere A = 4πr² = 4π × 20 × 20 = 1600π cm²

Calculation:

RP = RQ + PQ = 14.4 + 11.2 = 25.6

As we know,

RP × RQ = RT × RS

⇒ 25.6 × 14.4 = RT × 12.8

⇒ RT = 28.8 cm

Now, TS = RT – RS = 28.8 – 12.8 = 16 cm.

Total imports during the years = 125 + 145 + 165 + 188 = 623

Total exports during the years = 130 + 150 + 175 + 200 = 655

Balance difference = 655 – 623 = 32

∴ Average difference = 32/4 = 8

Shortcut Trick

Rate = 6% = 6/100 = 3/50

Ratio of Principal to Amount for 1 year = 50 : 53

Ratio of Principal to Amount for 2 years = (50)² : (53)² = 2500 : 2809

Given Amount = 2809 units = Rs. 280900 ⇒ 1 unit = Rs. 100

Principal = 2500 units = 2500 × 100 = Rs. 250000

∴ The correct answer is Rs. 250000.

Alternate Method

Given:

Amount (A) = Rs. 280900

Time (T) = 2 years

Rate (R) = 6% per annum

Formula Used:

A = P(1 + R/100)^T

Year 0 Year 1 Year 2

P = ? 280900

• 6%
• 6%

Amount = P × (53/50) × (53/50)

Calculation:

⇒ 280900 = P(1 + 6/100)²

⇒ 280900 = P(1 + 3/50)²

⇒ 280900 = P(53/50)²

⇒ 280900 = P × (2809 / 2500)

⇒ P = 280900 × (2500 / 2809)

⇒ P = 100 × 2500 = 250000

∴ The correct answer is Rs. 250000.

Additional Information

Compound Interest Formula

When interest is compounded annually, Amount A = P(1 + R/100)^T, where P is the principal, R is the rate of interest, and T is the time period in years.

Effective Rate of Interest

For 2 years, the effective compound interest rate can be directly calculated using the successive percentage change formula: R_eff = R + R + (R × R) ÷ 100.

Difference Between CI and SI

For 2 years, the difference between Compound Interest and Simple Interest on a sum P at rate R% is given by Diff = P(R/100)².

Total work = 96 units (LCM of 24, 16 and 32)

Hence, efficiency of A = 4 units, B = 6 units and C = 3 units

Work done by A and C in 6 days = (4 + 3) × 6 = 42 units

Remaining work = 96 – 42 = 54 units

Remaining work, B complete in = 54/6 = 9 days

As we know,

a² + b² – c² = 0, then

a⁶ + b⁶ – c⁶ = -3a²b²c²

Now,

$\frac{{2\left( {{a^6} + {b^6} - {c^6}} \right)}}{{3{a^2}{b^2}{c^2}}}$

$⇒ {\rm{}}\frac{{2 \times -3{a^2}{b^2}{c^2}}}{{3{a^2}{b^2}{c^2}}}$

⇒ -2

Important Points

a2 + b2 – c2 = 0

⇒ a² + b² = c²

cube both side

⇒ (a² + b²)³ = (c²)³

⇒ a⁶ + b⁶ + 3a²b²(a² + b²) = c⁶

⇒ a⁶ + b⁶ – c⁶ = – 3a²b²c²

Average speed = 50/9 km/hr

Using allegation method

10 km/hr 5 km/hr

50/9 km/hr

5/9 40/9

Time ratio to cover distance by bicycle to that of foot = 5/9 : 40/9 = 1 : 8

Now, (1 + 8) units = 9 hours

⇒ 1 unit = 1 hour

Hence, time taken by bicycle = 1 hour

Distance covered by bicycle = 10 × 1 = 10 km

Let the sum of last three terms be 3x.

According to the Question, the first term will be:

= 3x × 1/3 = x

Average of 4 terms is given as 30, i.e.

(Sum of 4 terms)/4 = 30

Sum of 4 terms = 120

From the above concluded data, we can write:

x + 3x = 120

4x = 120

x = 120/4

x = 30

First term is 30.

Formula Used:

Average = Sum of observations/Number of observations

Calculation:

Let the sum of n numbers be x, then

According to the question

x – 2n = 102     …(1)

x – 5n = 12     …(2)

Subtract equation (1) from equation (2)

3n = 90

⇒ n = 30

From equation (1)

x – 60 = 102

⇒ x = 102 + 60 = 162

∴ Average of first n numbers = 162/30 = 5.4

Given:

(cosecA + cotA + 1)(cosecA – cotA +1) – 2cosecA

Calculation:

(cosecA + cotA + 1)(cosecA– cotA +1) – 2cosecA

⇒ (cosecA + 1 + cotA)(cosecA + 1 – cotA) – 2cosecA

⇒ [(cosecA + 1)2 – cot2A] – 2 cosecA

⇒ cosec2A + 1 + 2cosecA – cot2A – 2cosecA

⇒ cosec2A – cot2A + 1

⇒ 1 + 1 = 2

Alternate Method

(cosecA + cotA + 1)(cosecA – cotA +1) – 2cosecA

Put A = 90°

(cosec90 + cot90 + 1)(cosec90 – cot90 +1) – 2cosec90

⇒ (1 + 0 + 1) (1 – 0 + 1) – 2

⇒ 2 × 2 – 2

⇒ 4 – 2 = 2

Let the length of the train X be l m and speed of train Y be x km/hr

As we know,

Time = Distance/speed

$72 = \frac{{225 + l}}{{\left( {60 - x} \right)\frac{5}{{18}}}}$     …1)

$18 = \frac{{225 + l}}{{\left( {60 + x} \right)\frac{5}{{18}}}}$     …2)

Multiply by 4 in equation (2)

$72 = \frac{{4\left( {225 + l} \right)}}{{\left( {60 + x} \right)\frac{5}{{18}}}}$     …3)

From equation (1) and equation (3)

$\frac{{4\left( {225 + l} \right)}}{{\left( {60 + x} \right)\frac{5}{{18}}}} = \frac{{225 + l}}{{\left( {60 - x} \right)\frac{5}{{18}}}}$

⇒ 4 (60 – x) = (60 + x)

⇒ 240 – 4x = 60 + x

⇒ 4x + x = 240 – 60

⇒ 5x = 180

⇒ x = 36

∴ Speed of train Y is 36 km/hr

From equation (1)

$72 = \frac{{225 + l}}{{\left( {60 - 36} \right)\frac{5}{{18}}}}$

⇒ 72 × 24 × 5/18 = 225 + l

⇒ 480 = 225 + l

⇒ l = 480 – 225

⇒ l = 255 m

∴ Length of train X is 255 m.

Distance covered by 1 round = perimeter of the circle

2πr = 1100

⇒ 2 × 22/7 × r = 1100

⇒ r = 1100 × 7/22 × 1/2

⇒ r = 175 cm

∴ Diameter of the wheel = 2 × 175 = 350 cm

As we know,

Volume of cuboid = Area of Base × Height

⇒ 15 × h = 330

⇒ h = 330/15

⇒ h = 22 cm

So, height of the cuboid is 22 cm.

Production by company l is 327, 326, 320, 318, and 310, which is continuously decreasing.

Total production of company II during the months = 180 + 179 + 160 + 167 + 150 = 836

Now, 20% of 836 = 836 × 1/5 = 167.2

So, in April month, company II have a contribution approximately 20% in the total fertilizer production.

The correct answer is option 3 i.e. end.

Meanings of the given options are-

• Abort means bring to a premature end because of a problem or fault. (किसी समस्या या दोष के कारण समय से पहले समाप्त करना)
• Eg- We need to abort the mission.
• Hate means feeling intense dislike. (तीव्र नापसंदगी महसूस करना)
• Continue means persist in an activity or process. (किसी गतिविधि या प्रक्रिया में बने रहना।)
• End means a termination of a state or situation. (किसी राज्य या स्थिति की समाप्ति)
• Eg-  There should be an end to violence.
• Begin means perform or undergo the first part of (an action or activity). ((किसी क्रिया या गतिविधि) का पहला भाग करना या करना।)

Clearly, 'end' is the synonym of the word.

The correct answer is option 3 i.e. heard.

• 'Had heard' is in the past perfect tense. Past perfect tense is used when we are talking about an action that took place before another past action. In the given sentence, there is no such mention.
• The sentence uses 'was' which indicates that it in the past tense and we need to use the past tense form of the verb i.e. heard.
  

So, 'heard' makes the sentence grammatically correct.

The correct answer is option 1 i.e. CDBA.

• C is the sentence that establishes the subject matter. Hence, it'll be the first sentence after rearrangement.
• D starts with 'even those' which refers to people mentioned in C. Hence, D follows C.
• Sentence B is the logical successor of D as it talks about people in the office mentioned in D.
• Last comes A as it uses 'also' and elaborates sentence B.

Sentences after rearrangement-

We can frequently find a large number of people sitting here and there and doing nothing. Even those who are employed often come late to office and leave early unless they are forced to be punctual. Once in office, they receive friends and relatives who call them any time without prior appointment. They also visit ailing friends and relatives or attend to personal matters even during office hours.

The correct answer is: Option 4 i.e. Surplus.

Key Points

• The word "Surplus" means having more than what is needed or used; an excess amount. (अधिशेष)
• Example: The farmer had a surplus of crops this year, more than he could sell.
• "Surplus" refers specifically to having an extra quantity of something that is more than what is required. (अधिशेष)
• Example: The company decided to use the surplus funds to invest in new technology.

Therefore, the correct answer is: Surplus.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Surroundings (परिवेश): The environment or area around a particular place.
• Example: She felt safe in the familiar surroundings of her hometown.
• Surcharge (अधिभार): An additional charge or payment.
• Example: The hotel added a surcharge for the extra services we requested.
• Surrogate (प्रतिनिधि): A substitute, especially a person deputizing for another in a specific role or office.
• Example: She acted as a surrogate during her colleague's maternity leave.

The correct answer is option 2.

• 'Send' is the base form of the verb and is mostly used in the present tense to give an order to someone. It is used in the active voice and an action that is occurring in the present.
• Eg- Send her gifts.
• 'Sent' is the past participle form of the verb and is used in the passive voice. It is also used to indicate an action that has occurred in the past.
• Eg- The letter has been sent.
• The given sentence indicates the action of sending must be done. It is not being done in the present. So, we must use 'sent' instead of 'send' to make the sentence correct.

The correct answer is option 4.

While changing the narration of an interrogative sentence, we need to follow steps-

• The boy is asking a question to Jane so, we must begin with 'the boy asked Jane'.
• Words like what, when, where, and how remain the same in indirect form.
• The second person form 'you' will be changed to 'she'.
• The sentence is in present continuous tense so it will be changed to past continuous tense. (was going)
• At last, line up the remaining parts.

Eventually, we get the sentence- ''The boy asked Jane what she was going to call the puppy.''

The correct answer is option 1 i.e. of.

Let us look at the usage of the prepositions-

• 'Of' is used to indicate the association between two things.
• 'In' is used when something resides within another thing.
• 'By' is used when something is done with the help of another thing.
• 'From' is used to indicate the starting point of an action.
• In the given sentence, the association between educational movement and village schools can be indicated by using 'of'.

Correct sentence-In a way, adult education is an educational movement through the medium of village schools.

The correct answer is option 1 i.e. villagers.

• In the previous sentence, the writer talks about village schools which indicates that education is being provided to villagers.
• Clearly, the required word must be 'villagers'.

​Correct sentence-  In the beginning, the villagers were suspicious.

The correct answer is option 3 i.e. them.

We require a pronoun that refers to the 'villagers'

• Him is used to refer to a singular male person.
• Us is used when the speaker is also a part of the group of people mentioned.
• Them is used as the object in the sentence to refer to a group of people.
• They is used as the subject in the sentence to refer to a group of people.

Clearly, 'them' will be used as we require a pronoun as the object in the sentence.

Correct sentence- It was hard to persuade them to realise that

The correct answer is option 3 i.e. from.

Let us look at the usage of the prepositions-

• For is used to indicate the reason.
• By is used when something is done with the help of another thing.
• From is used to indicate the origin.
• To is used to indicate the receiver of an action.

Clearly, 'from' will be used as the sentence highlights the origin as the schools.

Correct sentence-they were really getting something from the schools.

The correct answer is option 2 i.e. Children.

• The sentence talks about the people who had to leave their homes to go to schools.
• It is clear that those were the 'Children'.
• The whole passage is about adult education.

Correct sentence-They were not at all sure that they wanted their children to leave their homes.

The correct answer is option 1 i.e. indignation.

Meanings of the given options are-

• Indignation means anger about an unfair situation or about someone’s unfair behaviour
• Induction means the process or action of bringing about or giving rise to something.
• Indulgence means the action or fact of indulging.
• Indigenisation means bring (something) under the control, dominance, or influence of the people native to an area.

Clearly, 'indignation' is the correct word.